The Invariant Extended Kalman Filter as a Stable Observer
We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie gr...
Saved in:
| Published in | IEEE transactions on automatic control Vol. 62; no. 4; pp. 1797 - 1812 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
IEEE
01.04.2017
Institute of Electrical and Electronics Engineers |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 1558-2523 |
| DOI | 10.1109/TAC.2016.2594085 |
Cover
Loading…
| Abstract | We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie groups is that the estimation error is autonomous. In this paper we first generalize this result by characterizing the (much broader) class of systems for which this property holds. For those systems, the Lie logarithm of the error turns out to obey a linear differential equation. Then, we leverage this "log-linear" property of the error evolution, to prove for those systems the local stability of the IEKF around any trajectory, under the standard conditions of the linear case. One mobile robotics example and one inertial navigation example illustrate the interest of the approach. Simulations evidence the fact that the EKF is capable of diverging in some challenging situations, where the IEKF with identical tuning keeps converging. |
|---|---|
| AbstractList | We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie groups is that the estimation error is autonomous. In this paper we first generalize this result by characterizing the (much broader) class of systems for which this property holds. For those systems, the Lie logarithm of the error turns out to obey a linear differential equation. Then, we leverage this "log-linear" property of the error evolution, to prove for those systems the local stability of the IEKF around any trajectory, under the standard conditions of the linear case. One mobile robotics example and one inertial navigation example illustrate the interest of the approach. Simulations evidence the fact that the EKF is capable of diverging in some challenging situations, where the IEKF with identical tuning keeps converging. We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic non-linear observer on Lie groups, for continuous-time systems with discrete observations. One of the main features of invariant observers for left-invariant systems on Lie groups is that the estimation error is autonomous. In this paper we first generalize this result by characterizing the (much broader) class of systems for which this property holds. Then, we leverage the result to prove for those systems the local stability of the IEKF around any trajectory, under the standard conditions of the linear case. One mobile robotics example and one inertial navigation example illustrate the interest of the approach. Simulations evidence the fact that the EKF is capable of diverging in some challenging situations, where the IEKF with identical tuning keeps converging. |
| Author | Bonnabel, Silvere Barrau, Axel |
| Author_xml | – sequence: 1 givenname: Axel surname: Barrau fullname: Barrau, Axel email: axel.barrau@safrangroup.com organization: Groupe Safran, Safran Tech, Magny Les Hameaux, France – sequence: 2 givenname: Silvere surname: Bonnabel fullname: Bonnabel, Silvere email: silvere.bonnabel@mines-paristech.fr organization: Centre for Robot., PSL Res. Univ., Paris, France |
| BackLink | https://minesparis-psl.hal.science/hal-01692380$$DView record in HAL |
| BookMark | eNp9kDFrwzAQRkVJoUnavdBFawenOsmyrTGEpAkNZGg6i7N1JiqOU2QR2n9fh4QMHTodd3zvjnsjNmgPLTH2CGICIMzLdjqbSAHZRGqTikLfsCFoXSRSSzVgQyGgSIwssjs26rrPvs3SFIbMbHfEV-0Rg8c28vl3pNaR42_Y7LHlC99EChw7jvw9YtkQ35QdhSOFe3ZbY9PRw6WO2cdivp0tk_XmdTWbrpNKKROTHHMtARwSoHIpVXVKwuUqL0pwIjWapNKuLCVBVUMmNCqNmjIypKsKnRqz5_PeHTb2K_g9hh97QG-X07U9zfpXjFSFOEKfFedsFQ5dF6i-AiDsSZPtNdmTJnvR1CPZH6TyEaM_tDGgb_4Dn86gJ6Lrnf5ZpZRWvyzadTg |
| CODEN | IETAA9 |
| CitedBy_id | crossref_primary_10_1109_TVT_2022_3182017 crossref_primary_10_1016_j_ejcon_2024_101067 crossref_primary_10_1002_asjc_2089 crossref_primary_10_1109_LCSYS_2021_3064931 crossref_primary_10_1186_s43020_021_00061_z crossref_primary_10_1016_j_ifacol_2020_12_022 crossref_primary_10_1109_LRA_2023_3268043 crossref_primary_10_1016_j_ifacol_2023_10_1229 crossref_primary_10_1109_TAC_2024_3369549 crossref_primary_10_1016_j_automatica_2020_109464 crossref_primary_10_1109_ACCESS_2023_3280472 crossref_primary_10_1109_LRA_2023_3335775 crossref_primary_10_1016_j_automatica_2020_108812 crossref_primary_10_1017_S0373463322000443 crossref_primary_10_3390_aerospace10080708 crossref_primary_10_1109_JSEN_2022_3226327 crossref_primary_10_1049_cth2_12179 crossref_primary_10_1016_j_arcontrol_2021_11_002 crossref_primary_10_1109_TIM_2024_3522424 crossref_primary_10_1109_TAC_2021_3121247 crossref_primary_10_1007_s10291_018_0773_3 crossref_primary_10_1109_JSEN_2022_3174596 crossref_primary_10_1080_21642583_2024_2343303 crossref_primary_10_1109_ACCESS_2024_3466109 crossref_primary_10_1109_TMECH_2019_2891776 crossref_primary_10_1016_j_ifacol_2021_06_148 crossref_primary_10_1049_cth2_12166 crossref_primary_10_1109_TIM_2020_3027405 crossref_primary_10_1016_j_ifacol_2021_11_189 crossref_primary_10_1088_1361_6501_adbc0f crossref_primary_10_1109_LRA_2020_3005132 crossref_primary_10_1109_LRA_2023_3243520 crossref_primary_10_3390_s24123864 crossref_primary_10_1002_rnc_4984 crossref_primary_10_1016_j_ast_2021_107237 crossref_primary_10_1109_LRA_2024_3504320 crossref_primary_10_1109_TIM_2022_3225043 crossref_primary_10_1109_TRO_2018_2864788 crossref_primary_10_3390_s23136097 crossref_primary_10_1109_TIM_2022_3205673 crossref_primary_10_1007_s10291_023_01460_2 crossref_primary_10_1109_JSEN_2023_3319811 crossref_primary_10_1109_TAC_2022_3144328 crossref_primary_10_1109_TRO_2023_3272847 crossref_primary_10_1109_LRA_2024_3370006 crossref_primary_10_1109_JSEN_2023_3251389 crossref_primary_10_1109_JSEN_2023_3335964 crossref_primary_10_1088_1361_6501_ace377 crossref_primary_10_1109_TMECH_2023_3330908 crossref_primary_10_1002_rob_22349 crossref_primary_10_1109_LRA_2024_3511424 crossref_primary_10_1109_TIV_2020_2980758 crossref_primary_10_1016_j_fss_2021_07_003 crossref_primary_10_1109_JSEN_2020_3046718 crossref_primary_10_1109_TITS_2023_3309288 crossref_primary_10_1109_LRA_2024_3381088 crossref_primary_10_1109_LRA_2022_3194684 crossref_primary_10_1109_LRA_2025_3549664 crossref_primary_10_1146_annurev_control_061520_010324 crossref_primary_10_1109_TAC_2023_3328833 crossref_primary_10_1109_ACCESS_2020_2991465 crossref_primary_10_1109_TIM_2023_3239642 crossref_primary_10_1007_s11768_019_8028_6 crossref_primary_10_3390_machines10040265 crossref_primary_10_3934_jgm_2021015 crossref_primary_10_3390_rs15092286 crossref_primary_10_1016_j_ifacol_2017_08_061 crossref_primary_10_3390_s22207742 crossref_primary_10_1016_j_sysconle_2019_05_005 crossref_primary_10_3390_s24185899 crossref_primary_10_1109_LRA_2025_3548500 crossref_primary_10_1109_TMECH_2021_3090428 crossref_primary_10_1016_j_oceaneng_2025_120742 crossref_primary_10_1038_s41598_024_66282_9 crossref_primary_10_1109_TIM_2024_3449937 crossref_primary_10_3390_rs14246338 crossref_primary_10_1016_j_ifacol_2023_02_057 crossref_primary_10_1109_JSEN_2018_2808330 crossref_primary_10_1109_TRO_2021_3139964 crossref_primary_10_3390_electronics9030441 crossref_primary_10_1016_j_automatica_2022_110764 crossref_primary_10_1109_LCSYS_2024_3405485 crossref_primary_10_1109_JESTPE_2020_3008885 crossref_primary_10_1109_TMECH_2022_3175988 crossref_primary_10_1109_TIM_2024_3382751 crossref_primary_10_1016_j_dsp_2022_103820 crossref_primary_10_1109_TVT_2024_3405809 crossref_primary_10_1109_TAC_2020_2972213 crossref_primary_10_1007_s00521_023_08755_y crossref_primary_10_1017_S037346332100014X crossref_primary_10_1177_0278364919894385 crossref_primary_10_1016_j_measurement_2020_108707 crossref_primary_10_1109_LRA_2021_3085167 crossref_primary_10_1016_j_ifacol_2020_12_2438 crossref_primary_10_1109_TAES_2021_3133219 crossref_primary_10_1109_TCST_2023_3290299 crossref_primary_10_1109_TASE_2023_3314080 crossref_primary_10_1109_TASE_2024_3476069 crossref_primary_10_1016_j_measurement_2024_115854 crossref_primary_10_1137_19M1285974 crossref_primary_10_1016_j_automatica_2024_111688 crossref_primary_10_1016_j_oceaneng_2024_116898 crossref_primary_10_1177_09544100231169878 crossref_primary_10_1109_TMECH_2019_2959080 crossref_primary_10_1109_TRO_2021_3100156 crossref_primary_10_1109_TRO_2022_3165367 crossref_primary_10_1016_j_mechmachtheory_2023_105231 crossref_primary_10_1177_09544070221102662 crossref_primary_10_1109_LCSYS_2023_3237954 crossref_primary_10_1109_JSEN_2024_3452177 crossref_primary_10_1109_LRA_2023_3328450 crossref_primary_10_1109_TAC_2021_3086459 crossref_primary_10_1080_00207217_2020_1727026 crossref_primary_10_1109_TIM_2023_3250233 crossref_primary_10_1109_LCSYS_2022_3232562 crossref_primary_10_1109_TTE_2017_2755544 crossref_primary_10_1109_TVT_2019_2939679 crossref_primary_10_1016_j_jfranklin_2018_12_025 crossref_primary_10_1109_LRA_2023_3326700 crossref_primary_10_1016_j_measurement_2024_116136 crossref_primary_10_3390_s24206622 crossref_primary_10_1108_AEAT_05_2021_0150 crossref_primary_10_1109_TAES_2023_3285716 crossref_primary_10_1109_LRA_2020_2965391 crossref_primary_10_1109_LCSYS_2022_3178785 crossref_primary_10_1016_j_automatica_2021_109815 crossref_primary_10_1109_TRO_2020_3043970 crossref_primary_10_1109_JSEN_2023_3283793 crossref_primary_10_1109_TRO_2023_3309230 crossref_primary_10_1016_j_ifacol_2023_02_023 crossref_primary_10_1109_JSEN_2023_3317286 crossref_primary_10_1109_LRA_2020_3013854 crossref_primary_10_3390_jmse12071178 crossref_primary_10_1016_j_automatica_2023_111422 crossref_primary_10_1109_ACCESS_2024_3503901 crossref_primary_10_1109_JSEN_2023_3292427 crossref_primary_10_1109_JSEN_2021_3055536 crossref_primary_10_1109_TRO_2021_3063455 crossref_primary_10_3390_s22249853 crossref_primary_10_1109_TMECH_2020_3033530 crossref_primary_10_1109_TIM_2025_3550230 crossref_primary_10_1049_iet_spr_2020_0067 crossref_primary_10_1109_TRO_2023_3328202 crossref_primary_10_1109_LCSYS_2023_3340419 crossref_primary_10_1016_j_oceaneng_2023_116046 crossref_primary_10_1109_LRA_2020_3010214 crossref_primary_10_1109_TIV_2023_3287790 crossref_primary_10_1007_s11768_023_00158_7 crossref_primary_10_3390_s22239375 crossref_primary_10_1109_TAC_2022_3194094 crossref_primary_10_1109_TCST_2024_3351074 crossref_primary_10_1109_TMECH_2023_3252044 crossref_primary_10_3390_s24020597 crossref_primary_10_1016_j_ejcon_2025_101185 crossref_primary_10_1109_LRA_2024_3511374 crossref_primary_10_1109_LCSYS_2022_3172648 crossref_primary_10_1049_iet_rsn_2018_5252 crossref_primary_10_1109_JSEN_2025_3525469 crossref_primary_10_1080_00207721_2022_2096939 crossref_primary_10_1109_TAC_2019_2929112 crossref_primary_10_1146_annurev_control_060117_105010 crossref_primary_10_1109_LRA_2022_3224665 crossref_primary_10_1007_s11036_024_02381_1 crossref_primary_10_1016_j_ifacol_2024_08_468 crossref_primary_10_1109_ACCESS_2020_2979987 crossref_primary_10_1109_TIE_2022_3229335 crossref_primary_10_1109_JSEN_2018_2882714 crossref_primary_10_1109_LRA_2021_3139370 crossref_primary_10_1115_1_4055771 crossref_primary_10_1177_01423312221110956 crossref_primary_10_1109_JSEN_2022_3214293 crossref_primary_10_1016_j_robot_2022_104100 crossref_primary_10_1109_ACCESS_2023_3293158 crossref_primary_10_1109_TMECH_2022_3176015 crossref_primary_10_3390_s24196299 crossref_primary_10_1007_s10291_020_01076_w crossref_primary_10_1109_LRA_2024_3377950 crossref_primary_10_1109_TIM_2022_3196425 crossref_primary_10_1016_j_conengprac_2021_104926 crossref_primary_10_3390_s21010261 crossref_primary_10_1109_LRA_2024_3497757 crossref_primary_10_3390_s24051653 crossref_primary_10_3390_s18092855 crossref_primary_10_3390_machines9090182 crossref_primary_10_3390_s25061767 crossref_primary_10_1109_TIE_2023_3237872 crossref_primary_10_3390_aerospace11040268 crossref_primary_10_1016_j_oceaneng_2023_116511 crossref_primary_10_1002_rnc_6945 crossref_primary_10_1016_j_oceaneng_2024_117569 crossref_primary_10_1080_00207179_2022_2079004 crossref_primary_10_1016_j_arcontrol_2021_04_012 crossref_primary_10_1109_LRA_2024_3469808 crossref_primary_10_1109_LCSYS_2018_2886740 crossref_primary_10_1109_TAC_2021_3073323 crossref_primary_10_1109_TAC_2018_2846684 crossref_primary_10_1109_ACCESS_2022_3180769 crossref_primary_10_1109_JSEN_2018_2858276 crossref_primary_10_1016_j_automatica_2020_108858 crossref_primary_10_1142_S2737480724500183 crossref_primary_10_1109_TAES_2023_3290575 crossref_primary_10_1016_j_inffus_2022_08_013 crossref_primary_10_1109_JSEN_2024_3414995 crossref_primary_10_1016_j_conengprac_2019_104134 crossref_primary_10_3390_app13106187 crossref_primary_10_1016_j_sysconle_2019_03_001 crossref_primary_10_1109_TAC_2022_3173926 crossref_primary_10_1016_j_isatra_2022_12_014 crossref_primary_10_1021_acs_iecr_1c02916 crossref_primary_10_1109_LCSYS_2024_3506222 crossref_primary_10_1109_TITS_2022_3200938 crossref_primary_10_1109_LRA_2021_3102300 crossref_primary_10_1109_TITS_2023_3273391 crossref_primary_10_1155_js_5599534 crossref_primary_10_1109_TAES_2022_3197726 crossref_primary_10_1109_JSEN_2021_3108497 crossref_primary_10_1109_LRA_2024_3524905 crossref_primary_10_1016_j_ejcon_2024_101047 crossref_primary_10_3390_rs16163063 crossref_primary_10_1016_j_measurement_2023_112784 crossref_primary_10_31875_2409_9694_2022_09_03 crossref_primary_10_1016_j_automatica_2020_109244 crossref_primary_10_1002_cben_202000017 crossref_primary_10_1016_j_ifacol_2024_08_303 crossref_primary_10_1016_j_ifacol_2024_08_302 crossref_primary_10_1109_LRA_2025_3527346 crossref_primary_10_1109_TAC_2023_3346799 crossref_primary_10_1109_LRA_2021_3068694 crossref_primary_10_1016_j_ifacol_2024_08_300 crossref_primary_10_1109_LRA_2022_3210867 crossref_primary_10_3390_aerospace8090246 crossref_primary_10_1109_TIM_2023_3329103 crossref_primary_10_1016_j_ifacol_2023_12_072 crossref_primary_10_1109_LRA_2020_2966406 crossref_primary_10_5802_msia_25 crossref_primary_10_1109_ACCESS_2023_3237972 crossref_primary_10_1007_s11071_023_09030_4 crossref_primary_10_1007_s40815_019_00646_6 crossref_primary_10_1109_TIM_2025_3545191 crossref_primary_10_4236_jcc_2018_64006 crossref_primary_10_1177_09544100231157132 crossref_primary_10_1109_TAES_2024_3405928 crossref_primary_10_1109_TAC_2022_3179214 crossref_primary_10_1109_TCST_2021_3133080 crossref_primary_10_3390_s19020330 crossref_primary_10_1186_s13634_024_01172_w |
| Cites_doi | 10.1109/TAC.1968.1099024 10.1109/TAC.2003.812778 10.1109/CDC.2007.4434662 10.1109/TAC.2014.2336991 10.1017/CBO9780511546648 10.1109/TAC.2008.2006929 10.1007/3-540-36106-5_12 10.1109/9.566674 10.1007/BFb0036073 10.1109/TCST.2012.2195495 10.2514/3.56190 10.1016/S0005-1098(98)00053-3 10.1109/CDC.2009.5400372 10.1109/TAC.2009.2034937 10.1016/j.conengprac.2010.01.016 10.1016/j.sysconle.2009.11.008 10.1016/j.automatica.2014.08.010 10.2514/6.2010-8300 10.1016/j.automatica.2014.10.076 10.1109/CDC.2014.7040265 10.1109/TAC.2009.2020646 10.1109/CDC.2005.1582367 10.1109/TAC.2014.2342911 10.1109/TCST.2015.2413933 |
| ContentType | Journal Article |
| Copyright | Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | 97E RIA RIE AAYXX CITATION 1XC VOOES |
| DOI | 10.1109/TAC.2016.2594085 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 2005-present IEEE All-Society Periodicals Package (ASPP) 1998-Present IEEE Electronic Library (IEL) CrossRef Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE/IET Electronic Library url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1558-2523 |
| EndPage | 1812 |
| ExternalDocumentID | oai_HAL_hal_01692380v1 10_1109_TAC_2016_2594085 7523335 |
| Genre | orig-research |
| GroupedDBID | -~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 97E AAJGR AARMG AASAJ AAWTH ABAZT ABQJQ ABVLG ACGFO ACGFS ACIWK ACNCT AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ASUFR ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 EBS EJD F5P HZ~ H~9 IAAWW IBMZZ ICLAB IDIHD IFIPE IFJZH IPLJI JAVBF LAI M43 MS~ O9- OCL P2P RIA RIE RNS TAE TN5 VH1 VJK ~02 AAYOK AAYXX CITATION RIG 1XC VOOES |
| ID | FETCH-LOGICAL-c339t-7a75211dae1a3d4ecf4e0d7378b1d0495e235dbb2e1cf1605a35a5e6e9e5ccad3 |
| IEDL.DBID | RIE |
| ISSN | 0018-9286 |
| IngestDate | Fri May 09 12:25:20 EDT 2025 Tue Jul 01 03:36:05 EDT 2025 Thu Apr 24 22:58:05 EDT 2025 Wed Aug 27 02:52:18 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c339t-7a75211dae1a3d4ecf4e0d7378b1d0495e235dbb2e1cf1605a35a5e6e9e5ccad3 |
| ORCID | 0000-0002-6001-7766 |
| OpenAccessLink | https://minesparis-psl.hal.science/hal-01692380 |
| PageCount | 16 |
| ParticipantIDs | ieee_primary_7523335 crossref_citationtrail_10_1109_TAC_2016_2594085 hal_primary_oai_HAL_hal_01692380v1 crossref_primary_10_1109_TAC_2016_2594085 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2017-04-01 |
| PublicationDateYYYYMMDD | 2017-04-01 |
| PublicationDate_xml | – month: 04 year: 2017 text: 2017-04-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationTitle | IEEE transactions on automatic control |
| PublicationTitleAbbrev | TAC |
| PublicationYear | 2017 |
| Publisher | IEEE Institute of Electrical and Electronics Engineers |
| Publisher_xml | – name: IEEE – name: Institute of Electrical and Electronics Engineers |
| References | ref13 ref12 ref15 ref11 ref10 ref2 ref1 ref17 ref16 ref19 ref18 ref23 ref26 ref20 ref22 ref21 ref8 ref7 sonnemann reif (ref24) 1998; 34 ref9 ref4 ref3 song (ref25) 1995; 5 ref6 ref5 farrell (ref14) 2008 |
| References_xml | – ident: ref13 doi: 10.1109/TAC.1968.1099024 – ident: ref1 doi: 10.1109/TAC.2003.812778 – ident: ref6 doi: 10.1109/CDC.2007.4434662 – ident: ref10 doi: 10.1109/TAC.2014.2336991 – ident: ref15 doi: 10.1017/CBO9780511546648 – ident: ref8 doi: 10.1109/TAC.2008.2006929 – volume: 5 start-page: 59 year: 1995 ident: ref25 article-title: The extended Kalman filter as a local asymptotic observer publication-title: Estimation and Control – ident: ref19 doi: 10.1007/3-540-36106-5_12 – ident: ref11 doi: 10.1109/9.566674 – ident: ref12 doi: 10.1007/BFb0036073 – ident: ref3 doi: 10.1109/TCST.2012.2195495 – ident: ref21 doi: 10.2514/3.56190 – volume: 34 start-page: 1119 year: 1998 ident: ref24 article-title: An EKF-based nonlinear observer with a prescribed degree of stability publication-title: Automatica doi: 10.1016/S0005-1098(98)00053-3 – ident: ref9 doi: 10.1109/CDC.2009.5400372 – ident: ref20 doi: 10.1109/TAC.2009.2034937 – year: 2008 ident: ref14 publication-title: Aided Navigation GPS with High Rate Sensors – ident: ref17 doi: 10.1016/j.conengprac.2010.01.016 – ident: ref26 doi: 10.1016/j.sysconle.2009.11.008 – ident: ref18 doi: 10.1016/j.automatica.2014.08.010 – ident: ref23 doi: 10.2514/6.2010-8300 – ident: ref16 doi: 10.1016/j.automatica.2014.10.076 – ident: ref4 doi: 10.1109/CDC.2014.7040265 – ident: ref7 doi: 10.1109/TAC.2009.2020646 – ident: ref22 doi: 10.1109/CDC.2005.1582367 – ident: ref5 doi: 10.1109/TAC.2014.2342911 – ident: ref2 doi: 10.1109/TCST.2015.2413933 |
| SSID | ssj0016441 |
| Score | 2.6662142 |
| Snippet | We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear observer on Lie groups,... We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic non-linear observer on Lie... |
| SourceID | hal crossref ieee |
| SourceType | Open Access Repository Enrichment Source Index Database Publisher |
| StartPage | 1797 |
| SubjectTerms | Asymptotic observers Automatic Convergence Differential equations Engineering Sciences Estimation error Kalman filters Mathematical model nonlinear filters Observers Trajectory |
| Title | The Invariant Extended Kalman Filter as a Stable Observer |
| URI | https://ieeexplore.ieee.org/document/7523335 https://minesparis-psl.hal.science/hal-01692380 |
| Volume | 62 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LT9tAEB4lnOAALVAR-tAK9YKEE--u7bWPESIKLSkXIuVm7XrHKmpqECQc-us7YxsLEELcrNVaGs2MPe9vAL7LMPXKGxX40Oog4j6qFFMZ2Izcc9RehZZnh2e_kuk8-rGIFz046WZhELFuPsMhP9a1fH9TrDlVNjIUNWkd96FPgVszq9VVDNiuN39d-oBV2pUkw2x0NT7lHq5kSK4-A3o9M0H939wA-WSzSm1YJjsweySp6Sf5M1yv3LD49wKt8b00f4Dt1sMU40YlPkIPq13YeoI7uAcZKYc4rx4oTibGirM2ES5-2uVfW4nJNZfQhb0XVpAz6pYoLh1nb_FuH-aTs6vTadDuUAgKrbNVYCwRIKW3KK32ERZlhKE32qROeooOYlQ69s4plEUpKbaxOrYxJphhTML1-hNsVDcVHoAwTmtjwqhMMxd5ZVOZoExKmTmpTGnLAYwe2ZoXLcA477lY5nWgEWY5CSJnQeStIAZw3L1x24BrvHH3iCTVXWNU7On4IuczBpQhzyN8kAPYYwl0t1rmH75-_Bk2FRvpug_nC2ys7tb4lVyMlftW69Z_q9nKGA |
| linkProvider | IEEE |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1La9tAEB6S9NDm0LRNS9xHspReCpWt3ZW00tGYGCexk4sNuYld7YiUukpxbR_66zsjKSIJpeQmlhUMMyPN-xuALzJMvfJGBT60Ooi4jyrFVAY2I_cctVeh5dnh2WUyWUTn1_H1DnzrZmEQsW4-wz4_1rV8f1tsOFU2MBQ1aR3vwjOy-7FsprW6mgFb9ua_S5-wSruiZJgN5sMRd3ElfXL2GdLrgRHaveEWyHu7VWrTMj6A2R1RTUfJj_5m7frFn0d4jU-l-hW8bH1MMWyU4jXsYPUG9u8hDx5CRuohzqotRcrEWnHapsLFhV3-tJUYf-ciurC_hRXkjroliivH-VtcvYXF-HQ-mgTtFoWg0DpbB8YSAVJ6i9JqH2FRRhh6o03qpKf4IEalY--cQlmUkqIbq2MbY4IZxiRer9_BXnVb4REI47Q2JozKNHORVzaVCcqklJmTypS27MHgjq150UKM86aLZV6HGmGWkyByFkTeCqIHX7s3fjXwGv-5-5kk1V1jXOzJcJrzGUPKkO8RbmUPDlkC3a2W-e__fXwCzyfz2TSfnl1efIAXik123ZXzEfbWqw1-Iodj7Y5rPfsLZjTNYQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+Invariant+Extended+Kalman+Filter+as+a+Stable+Observer&rft.jtitle=IEEE+transactions+on+automatic+control&rft.au=Bonnabel%2C+Silvere&rft.au=Barrau%2C+Axel&rft.date=2017-04-01&rft.pub=Institute+of+Electrical+and+Electronics+Engineers&rft.issn=0018-9286&rft.volume=62&rft.issue=4&rft.spage=1797&rft.epage=1812&rft_id=info:doi/10.1109%2FTAC.2016.2594085&rft.externalDBID=HAS_PDF_LINK&rft.externalDocID=oai_HAL_hal_01692380v1 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0018-9286&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0018-9286&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0018-9286&client=summon |